Research article
04 Aug 2017
Research article | 04 Aug 2017
An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces
Valentina Castellanos-Rodríguez1,2, Eric Campos-Cantón2,3, Rafael Barboza-Gudiño1, and Ricardo Femat2
Valentina Castellanos-Rodríguez et al.
Valentina Castellanos-Rodríguez1,2, Eric Campos-Cantón2,3, Rafael Barboza-Gudiño1, and Ricardo Femat2
- 1Instituto de Geología, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México
- 2Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, México
- 3Mathematics Department, University of Houston, Houston, Texas 77204-3008, USA
- 1Instituto de Geología, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México
- 2Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, México
- 3Mathematics Department, University of Houston, Houston, Texas 77204-3008, USA
Correspondence: Castellanos-Rodríguez Valentina (valentina@cimat.mx)
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Received: 05 Oct 2016 – Discussion started: 14 Nov 2016 – Revised: 18 May 2017 – Accepted: 14 Jun 2017 – Published: 04 Aug 2017
The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich–Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone – where slow earthquakes are generated within the frictionally unstable region – is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.